The intuition that complex learning systems are unreliable due to their inscrutable complexity will become moot once we train them to generate proof for their solutions.
These are not the conditions under which you can prove correctness of the classification result (and no human can do that either). But you can prove the properties of the algorithm that you use to classify your data.
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Facial recognition is not a domain in which you will get provably correct results, until you can reconstruct an individual genotype from the phenotype. However, you may show that a feature learning algorithm extracts at least as much information as a reference algorithm.
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